Some memory systems, such as solid-state drives (SSDs), contain one or more memory dies having blocks of memory that can be read or written in parallel. Memory systems typically have a maximum peak current limit. For example, some USB devices have a maximum peak current limit of 800 mA, while some SD cards have a maximum peak current limit of 400 mA. The limits can restrict the number of memory dies that can be operated in parallel. Further, in a multi-die environment, all memory dies are typically trimmed to program at the same speed regardless of how many dies are active at the same time. Some memory systems have a low-peak current mode that is activated with a special command (e.g., CMD_B2h), in which a lower peak value is set based on a ROM fuse parameter. This lower peak value is applied to all of the memory dies in the memory system and over the entire program operation.